Simplify the following expression: $ q = \dfrac{r + 6}{-2r} + \dfrac{-7}{4} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{r + 6}{-2r} \times \dfrac{4}{4} = \dfrac{4r + 24}{-8r} $ Multiply the second expression by $\dfrac{-2r}{-2r}$ $ \dfrac{-7}{4} \times \dfrac{-2r}{-2r} = \dfrac{14r}{-8r} $ Therefore $ q = \dfrac{4r + 24}{-8r} + \dfrac{14r}{-8r} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{4r + 24 + 14r}{-8r} $ $q = \dfrac{18r + 24}{-8r}$ Simplify the expression by dividing the numerator and denominator by -2: $q = \dfrac{-9r - 12}{4r}$